perlov0 wrote:
they weigh the same. I'll edit my post with a new riddle soon
EDIT:
How many 5-digit numbers are there that do not contain the numbers 3 and 5, and are multiples of 4?
(It cannot start with 0, ie. 01234 is not a 5 digit number)
I couldn't find this to be a trick question, so I'm going to try to answer it straight up. Are there
1,176 5-digit numbers falling under those specifications? I found there to be 21 of 25 qualifying numbers that were multiples of 4 from 1 to 100 (excluding 32, 36, 52, 56; Multiples of 4 will never END with a 3 or a 5). Then I applied this to the range 1 to 1000 and got 168 qualifying numbers out of 250 (Take 21 and multiply it by 8, which excludes the numbers from 300-399 and 500-599). So I used that to find how many were in 5-digit numbers, or tens of thousands, multiplying 168 by 7, which excludes numbers from 0-9,999; 3,000-3,999; and 5,000-5,999.
EDIT: After reading over the solution above, I realize that I have not calculated the answer correctly, or specifically, I simply have not
finished calculating. What I must do is multiply 168 by 8, to account for all multiples of 4 in the range of 1-9,999, excluding 3,000-3,999 and 5,000-5,999. This yields a result of 1,344 multiples. I must then mutiply this number by 7, to account for all multiples of 4 in the range of 1-99,999, excluding 1-9,999; 30,000-39,999; and 50,000-59,999.
The result: the total number of multiples of 4 in the range of all 5-digit integers, not including those with a 3 or a 5 for at least one of the digits, is
9408.
And sorry for double-posting.